Construction and Restrictions of Consistent Matrices by Macharis’ Method

Abstract

In 2004, Macharis et al. proposed a consistent comparison matrix. In this study, we provide a patch work for discussing the construction and restrictions of their consistent comparison matrix. Their study is important in academia and has been cited by over 200 papers. However, in the article, the authors neither provide a detailed explanation on how to construct the proposed revised consistent comparison matrix nor mention any restriction when constructing it. In this study, we not only propose an algorithm to construct the consistent matrix, but also prove that two restrictions exist when developing a sequence of their consistent comparison matrices, which are: (a) the changing of entries should follow a decreasing order with respect to the row index and (b) there is at most one entry in each row that can be revised by experts. The results of this study will help researchers properly apply the consistent matrices proposed by Macharis et al. (2004) in the future.

Construction of Consistent Comparison Matrix by Macharis’ Method Revisit

“…It indicates that the AHP-PROM-ETHEE method is a hot research problem for decisionmaking problems. Since Chu et al [9] had already provided a comprehensive literature review for those papers published before 2018, we will only examine those 152 papers published after 2018.…”

“…In the second category, this paper paid attention to the problem of changing entries in a consistent comparison matrix by experts and then adjusting entries to preserve the consistent property. We list him in the following: Chu et al [9], specifically.…”

“…Chu et al [9] pointed out that Macharis et al [1] provided a consistent comparison matrix and then informed readers the expert wanted to change three entries. Macharis et al [1] provided the results for the first two changes, but Macharis et al [1] did not show how to execute their change.…”

“…Macharis et al [1] provided the results for the first two changes, but Macharis et al [1] did not show how to execute their change. Chu et al [9] developed their method to satisfy the preassigned value by the expert and still result in a consistent matrix. Moreover, Chu et al [9] showed that two extra conditions must be kept to run the changing entries of a consistent comparison matrix.…”

“…Chu et al [9] developed their method to satisfy the preassigned value by the expert and still result in a consistent matrix. Moreover, Chu et al [9] showed that two extra conditions must be kept to run the changing entries of a consistent comparison matrix. e detailed explanation of Chu et al [9] will be presented in Section 2.…”